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Journal ArticleDOI

Low Space Order Analysis of Radial Pressure in SPMSM With Analytical and Convolution Approaches

12 Jul 2016-IEEE Transactions on Magnetics (IEEE)-Vol. 52, Iss: 11, pp 1-7

Abstract: This paper presents an analysis of low space order of the air-gap radial Maxwell pressures in surface permanent magnet synchronous machines with fractional slot concentrated windings. The air-gap Maxwell pressures result from the multiplication of the flux density harmonics due to magnetomotive forces and permeance linked to the magnet, the armature, and the stator slots and their interactions. One low space order is selected, and different approaches are compared to determine the origin of this pressure. First, an analytical prediction tool analytical calculation of harmonic force orders (ACHFO) is used to calculate the space and time orders of these magnetic pressure harmonics while identifying their origin in terms of interactions between magnet, armature, and teeth effects. In addition, the analytical prediction of ACHFO is compared with the flux density convolution and finite-element approaches. The main advantage of our tool is the speed of computation. Finally, an experimental operational deflection shape measurement is performed to show the deflection shape of the low space order selected.
Topics: Magnetic flux (55%), Harmonics (53%), Stator (53%), Magnetic pressure (53%), Armature (electrical engineering) (52%)

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Low space order analysis of radial pressure in SPMSM
with analytical and convolution approaches.
Patricio La Delfa, Mathias Fakam, Michel Hecquet, Fréderic Gillon.
Laboratory of Electrical Engineering and Power Electronics, L2EP, Ecole Centrale de Lille,
Cité scientifique, CS20048, 59651 Villeneuve d’Ascq Cedex-France.
Abstract This paper presents an analysis of low the space order of the air-gap radial Maxwell pressures in Surface Permanent
Magnet Synchronous Machines (SPMSM) with fractional slot concentrated windings. The air-gap Maxwell pressures result from the
multiplication of the flux density harmonics due to magnetomotive forces and permeance linked to the magnet, the armature, and the
stator slots and their interactions. One low space order is selected and different approaches are compared to determine the origin of this
pressure. First, an analytical prediction tool ACHFO (Analytical Calculation of Harmonic Force Orders) is issues to calculate the space
and time orders of these magnetic pressure harmonics while identifying their origin in terms of interactions between magnet, armature
and teeth effects. Additionally, the analytical prediction of ACHFO is compared with the flux density convolution and finite element
approaches. The main advantage of our tool is the speed of computation. Finally, an experimental Operational Deflection Shape
measurement (ODS) is performed to show the deflection shape of the low space order selected.
Keywords fractional slot concentrated winding, air-gap radial Maxwell pressures; lowest space order; analytical tool; convolution
analysis; operational deflection shape (ODS).
I. INTRODUCTION
The commitment of many countries to reduce
greenhouse gas emissions and preserve primary energy
resources has significantly contributed to the
development of hybrid and electric transport. The use of
concentrated winding permanent magnet synchronous
machines in transport applications in which speed
variation is required increases efficiency and power
density. It is essential to take into account both the
electrical characteristics designing electrical machines
and the electromagnetic acoustic noise radiated. This
source of audible noise arises when Maxwell pressures
induce dynamic deflections of the external structure
(stator or rotor), which then propagate in the ambient air
as acoustic waves [1], [2].
One goal of this research is to identify and analyse the
low space order of the air-gap radial pressure (Maxwell
pressure), i.e. the harmonics specific to the magnets, the
armature, and the teeth and their interactions which we
call specific effects. Many references provide analytical
relations in order to evaluate radial pressures. Each
harmonic of this radial pressure is well-known [2], [3],
[5], [11], for example, coupled with the interaction
between the slotting and the magnetomotive force
(MMF), or the saturation effect [4], [6].
On the other hand, the contribution of each air-gap
flux density B(t,α
s
) harmonic to identify the origin of
each harmonic radial pressure is not easy. Also the origin
of each radial pressure harmonic component is required.
Indeed many contributions of specific effects linking the
interactions between armature, rotor and permeance
effects are combined. In [7] and [8] the author gives
different contributions for each harmonic of the pressure
but without a slotting effect, in the case of synchronous
machines with magnets (IPM and SPM).
Analytical models (permeance / magnetomotive force
and winding function approaches) [3], [5], semi-
analytical subdomain models [9] and the finite element
method can be used to evaluate the airgap flux density.
The latter two approaches are precise and it is possible to
deduce the tangential and radial components of flux
density.
In this paper, only the origin of the radial pressure is
investigated. Our approach is described and illustrated
on a Surface Permanent Magnet Synchronous Machine
(SPMSM) with fractional slot concentrated windings. A
tool named ACHFO (Analytical Calculation of
Harmonic Force Orders) is applied to predetermine and
identify all the sources of the radial pressure only for the
low space orders established by specific effects, the
interaction effects mentioned previously, and their own
carrier frequencies. The ACHFO tool does not use air-
gap flux density but only the harmonics of permeance,
rotor and stator MMF and their interactions. At last,
ACHFO cannot determine the amplitude and the phase
of space orders [10]. Although the tool gives a complete
picture of each harmonic of the radial pressure versus
time and space orders, some of them have no influence
on the magnetic noise [11], [12], [13].
In order to validate the origin of the radial pressure,
different approaches are compared such as the
convolution approach [14]. In addition, an experimental
Operational Deflection Shape measurement (ODS) is
performed to show the deflection shape of the low space
order.

II. SCOPE OF THE WORK
A. Description of the machine studied
The structure is presented in figure 1, a modular
machine defined by 2p=Z
s
± 2, (Zs number of slots fixed
to Z
s
=12, pole pair number p=5).
Fig. 1: SPMPM Machine and flux lines by FEM.
What is more, this machine is characterized by a
winding factor k
w
(1) = 0.933, S
pp
=0.4, Least Common
Multiple (lcm) = 60, and Geatest Common Divider (gcd)
= 2. The winding factor K
w
and the number of slots per
pole per phase S
pp
are given in [15]. It also gives the lcm
and the gcd described as used in [11], [16]. The slot-pole
combination is important in terms of vibration generation
as shown in [8], [13], [17]. The gcd, between the number
of slots and pole pair number, corresponds to the lowest
dominant non-zero of the magnetic radial pressure
harmonics.
A tooth concentrated winding SPMSM is chosen for
its high power density and high efficiency although it
makes it harder to obtain a high slot fill factor, since
there are two layers per slot. The winding pattern is
designed using a star of slots methodology [18], and the
author [19] analyse the windings configuration on
fractional-slots PMSM performance.
The star of slots consists in installing and connecting
the elementary windings to conform to the phases shift
between the three phases of the supply and guarantee
maximal electromagnetic torque.
Fig.2: Phase 1 (4 coils around T1, T2, T7 and T8)
Phase 1 shown in figure 2 illustrates the elementary
windings installed on teeth T1, T2 and diametrically
opposed teeth T7, T8. Both real and imaginary
elementary fundament electromotive forces (EMF) are
equal to 1 and the resulting phase 1 EMF is shown in
figure 3.
Fig. 3: Phase 1 (Elementary winding and resultant EMF)
First, we present all the harmonics of the radial
pressures of this machine through a 2D finite element
calculation. This calculation will be the reference and the
lowest order will be selected for a discussion of these
origins by regarding the different approaches to be
compared. The aim is to select a fast and effective
approach to optimize the structure.
III. FINITE ELEMENT SIMULATIONS
The finite element simulations include the rotational
movement of the machine and the coupling with the
circuit, (i.e. phase resistor, synchronous inductance and
inductance head winding). The power supply is
sinusoidal.
A. Air-gap radial flux density
The FE electromagnetic model determines the
distribution in time and space of the radial air-gap flux
density B(t,α
s
) with α
s
being the stator mechanical
angle.
We defined a line in the centre of air-gap for each
time value (200 points per period). It determines the flux
density B(α
s
): 360 points divided by 2.
According to (1), it also determines B
aR
(t,α
s
) and
B
pm
(t,α
s
), the armature and magnet radial flux density,
respectively [2]. Note the flux density B
aR
is obtained by
considering the magnet flux density as equal to zero and
the magnet relative permeability is retained. In this study
only the radial components is taken into to account.
Indeed, [20] shows that radial and tangential flux
densities have the same orders and frequencies.
B
(t,α
s
) = B
aR
(t,α
s
)+ B
pm
(t,α
s
) (1)
B
aR
(t,α
s
) = ∑
(B
υ
cos(υpα
s
± kωt)) (2)
B
pm
(t,α
s
) = ∑(B
μ
cos(μpα
s
± kωt+ϕ
μ
)) (3)
υ, μ : armature and permanent magnet space orders
ϕ
μ
: Both angle rotor /stator for same order considered [rad].
T2
T1
T7
T8
T1
T2
T8
T7

B. Air-gap Radial pressure.
On the base of the air-gap radial flux density versus
time and space, the air-gap radial Maxwell pressure
σ(t,α
s
) can be approximated by relation (4).
σ (t,α
s
)
{B(t,α
s
)}² / (2μ
0
) (4)
The global air-gap radial pressure shown in figures
4(a-b),versus space and time, estimated from the global
air gap flux density reveal large number of harmonics.
Figure 4(c-d) shows only the armature radial pressure
and figure 4(e-f), only the magnet radial pressure. Note
the different FFT give absolute values for the
magnitudes.
Fig.4a: Global Air-gap radial pressure σ(α
s
) versus space
Fig.4b: Global air-gap radial pressure σ(t) versus time
We obtain harmonics H
10
, H
12
which represent 2p
poles and the number of slots Z
s
, respectively. Low
orders H
2
and H
4
are also shown.
Fig.4c: Armature radial pressure σ
aR
s
) versus space
Fig.4d: Armature radial pressure σ
aR
(t) versus time
Fig.4e: Armature radial pressure σ
pm
s
) versus space

Fig.4f: Armature radial pressure σ
pm
(t) versus time.
Figure 5 depicts the lowest space orders of the
global air-gap radial pressure FFT 2D versus time and
space for the nominal working point. A space order 2 at
2fs is shown, noted (2, 2fs). Also shown are negative
pressure rays at (-2, 4fs), (-4, 2fs) and positive rays at (4,
4fs) which produce opposing revolving vibratory waves.
Fig. 5: FFT 2D of the air-gap radial pressure (global case)
The modular machine studied gives the gcd = 2, which
corresponds to the dominant lowest non-zero pressure
order 2 found in simulations. The previous figure
illustrates the higher order 2 at 2fs magnitude.
IV. ORIGIN OF RADIAL AIR-GAP PRESSURE
The objective of this section is to understand the
origin of a pressure line for the lowest space order. In
electrical machines, it can be linked to many effects and
their combination (teeth, stator and rotor field, etc). The
origin of about order 2 to 2fs determined by different
approaches will be compared. Initially, Matlab tool that
incorporates all the harmonics of the radial pressure is
developed. The interest of this is that it determines each
pressure line produced quickly.
A. Analytical Calculation of Force Orders (ACHFO)
The ACHFO tool disregards eccentricity, and
considers a smooth rotor link to the surface permanent
magnet machine. It identifies all the space orders and
frequencies of the air-gap Maxwell pressure harmonics
in a given electrical machine. It also tracks the origin of
the lowest space orders, i.e. combined interactions
between the armature, magnets and slotting effects, and
its own interactions too. In relation (5), the flux density
is calculated by the product ofthe air-gap permeance per
unit of surface by the magnetomotive forces for the rotor
(magnet) and the stator (concentrated winding).
Note in (6), A
ξ
represents the ξ
th
slotting permeance
per unit [3]. The air-gap permeance is linked versus
space only, the rotor is smooth [20].
σ(t,α
s
)
1/2μ
0
* {Λ(α
s
)*[F
r
(t,α
s
)+ F
s
(t,α
s
)] (5)
With :
Λ(α
s
)=
Λ
0
/2
+ (μ
0
/e)k
c
(ξ)
A
ξ
cos(ξZ
s
α
s
) (6)
ξ
th
= {0,1,3,5,…}
F
r
(t,α
s
)=∑
(k)
f
mμ
cos(μpα
s
± ωt+ϕ
μ
) (7)
µ
th
= {1,3,5,…}
F
s
(t,α
s
)=∑
(k)
f
m
υ
cos(υpα
s
± ωt) (8)
th
= {1,3,5,…}
σ(t,α
s
)
1/2μ
0
*Λ(α
s
)²*F
r
(t,α
s
)² + 1/2μ
0
*Λ(α
s
)²* F
s
(t,α
s
+ 1/μ
0
*Λ(α
s
)²*F
r
(t,α
s
)* F
s
(t,α
s
). (9)
υ,μ,ξ: Space order armature/permanent magnet/permeance
Consequently, we can obtain the relationship (9) that
reveals three families of space classified into three
groups:
-the first one represents the multiplication of several
air-gap permeance waves by several rotor
magnetomotive force waves only (F
r
).
-the second one represents the multiplication of
several air-gap permeance waves by several stator
magnetomotive force waves only (F
s
).
-the third one represents the multiplication of several
air-gap permeance waves by both F
r
and F
s
waves.
Table 1 summarizes the analytical formulations used
by the ACHFO tool. Note that the ACHFO analytical
tool does not take into account the magnitude of the
pressure waves. The tool gives the origin of the
harmonics (2,2fs) in Table 2.
To conclude this part, the air-gap pressure low order
2 at 2fs represents the total effects given by ACHFO, i.e.
linked armature order, magnets-permeance, magnets-
armature and magnet-permeance-armature interactions.
Analysis of table 2 reveals that the order (2,2fs) does not
result only from magnet-armature interaction, which
means that it also has a load origin.

TABLE 1: PRESSURE HARMONICS
Effect/ Group
Order radial pressure:
Frequency:
Due to magnets :
Own interaction :
2 μ
th
p
and μ
th
={1,3,5,7. .}= (2k+1)
(μ
1
±μ
th
)p ; μ
1
=1
2fs (1+2k);
k={0,1,2, }
(μ
1
±μ
th
).fs
Due to armature :
Own interaction :
2υ
th
; υ
th
=6k±1;
(υ
1
± υ
th
) k = {0, 1, 2..}
2fs
2fs
Interactions due to
Magnet and permeance:
2(μ
th
p±μ
th
Z
s
), μ
th
={1,3,5,7..}
(μ
th1
± μ
th
) p ± ( ξ
2
±ξ
1
) Z
s
(μ
th
± μ
th
).p±ξ.Z
s
ξ = {0,1, 3, 5…}
2μ
th
fs
2fs(μ
th1
± μ
th
)
(μ
th
± μ
th
).f
s
Armature-Magnets:
(μ
th
.p)± υ
th
( μ
th
±1).f
s
Magnets- Permeance-
Armature-:
(p.µ
th
) ± (ξ.Z
s
) ± υ
th
;
th
±1).f
s
TABLE 2: ANALYTICAL ORDERS PRESSURE RESULTS
Orders ± 2 at 2fs
th
p
1
±μ
th
)p
2υ
th
(υ
1
±υ
th
)
2(μ
th
p±μ
th
Z
s
)
th
±μ
th
) p ± (ξ
2
± ξ
1
) Z
s
(μ
th
± μ
th
).p±ξ.Z
s
(μ
th
.p)± υ
th
(p.µ
th
) ± (ξ.Z
s
) ± υ
th
;
ξ={0,1,3,…}
The table also gives the details of the second group of
harmonics given by H
υ
1 (first harmonic armature effect)
and H
υ
5, H
υ
11, linked to specific harmonics υ=6k±1
with k={0,1,2,3..} called stator slots harmonics [3], [7].
The third group of interactions involving permeance
and rotor and stator magnetomotive forces harmonics is
also responsible for the generation of order 2. Harmonics
H
υ
1 and H
μ
1, H
ξ
1, are related to the armature and
interactions due to the magnet- slotting permeance, and
H
υ
5, H
μ
3, H
υ
17, H
μ
11 are related to the magnet-
permeance-armature considering respectively ξ=1 and
ξ =3, respectively, as permeance harmonics.
The interaction of armature and magnet effects
generates H
μ
1(*p), H
υ
7, and H
μ
3(*p), H
υ
17. Considering
the number of pole pairs p (see Table 2) the armature-
magnet interaction H
μ
1 is equal to H
μ
5 which represents
the number of pairs of poles. Following the same
reasoning the harmonic H
μ
3 is equal to H
μ
15.
Additionally, the ACHFO tool determines the space
orders and frequencies of the radial flux density as
detailed in Table 3. Figure 6 illustrates the radial flux
density 2D FFT obtained from the FE electromagnetic
model. It validates the previous analytical flux density
results. These results can be used for the second
approach with the convolution product.
TABLE 3: ANALYTICAL ORDERS FLUX DENSITY RESULTS
Fig.6: Air-gap radial flux density 2D-FFT
B. Convolution product.
In order to compare our ACHFO results (Table 1 and
2), we use another approach: the convolution approach.
This approach as given in [14], is based on the two-
dimensional Direct Fourier Transform (2D-DFT) of the
air-gap radial flux density and its convolution with itself
(10). This approach considers the radial flux density
from FE simulation and is characterized by considerable
simulation and computing time when taking into
accounts all the orders. However, this approach offers
the possibility of determining the amplitude and the
phase of the radial pressure for each low order and
justifies the order 2 progressive wave of mechanical
deformation, as shown in the experimental part (figure
11 a-d).
σ
2DFT
(r,f) =1/2μ
0
*[B
2D-DFT
(k
1
,f
1
)*B
2D-DFT
(k
2
, f
2
)] (10)
r: Space order radial pressure by convolution approach.
Figure 7 represents the radial pressure space orders
and frequency obtained by the convolution methodology.
The air-gap flux density is calculated by the finite
element method for the studied modular machine and we
obtain the same results as in figure 5.
(7,fs)
(-5,fs)
Flux density H
Bμ,
υ
Orders at μ
th
fs
Magnets
(H
Bμ
; f ) =( μ
th
*p ; μ
th
fs)
(H
Bμ
-5 ; fs) and (H
Bμ
-15 ; 3fs)
Armature
(H
; f) = (2υ
th
-1 ; fs)
(H
Bυ
1 ; fs) and (H
Bυ
9 ; fs),
Interaction Magnets -Permeance
(H
Bμξ
;f)=(ξZ
s
±μ
th
p; μ
th
fs)
(H
Bμξ
-3 ; 3fs), (H
Bμξ
7 ; fs),
(H
Bμξ
-17; fs), (H
Bμξ
19; fs), (H
Bμξ
9; 3fs),…

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Journal ArticleDOI
Abstract: Abstract The electromagnetic noise generated by the Maxwell radial pressure is a well-known consequence. In this paper, we present an analytical tool that allows air gap spatio-temporal pressures to be obtained from the radial flux density created by surface permanent magnet synchronous machines with concentrated winding (SPMSM). This tool based on winding function, a global air-gap permeance analytical model and total magnetomotive force product, determines the analytical air-gap spatio temporal and spectral radial pressure.We will see step-by-step their impacts in generating noise process. Also two predictive methods will be presented to determine the origin of the lows radial pressure orders noise sources. The interest lies in keeping results very quickly and appropriate in order to identify the low order electromagnetic noise origin. Then through an inverse approach using an iterative loop a new winding function is proposed in order to minimize radial force low order previously identified and chosen.

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Journal ArticleDOI
Jerome Cros1, Philippe Viarouge1Institutions (1)
Abstract: The windings concentrated around the teeth offer obvious advantages for the electrical machines with radial air-gap, because the volume of copper used in the end-windings can be reduced. The Joule losses are decreased, and the efficiency is improved. These machines are still limited to applications of sub-fractional power and they generally present a reduced number of phases. In the three-phase machines, the concentrated winding is too often restricted to a winding with a short pitch of 120 electrical degrees, i.e., to a winding with performances reduced compared to the traditional structures. But there is a significant number of three-phase structures which can support a concentrated winding if the number of poles is increased. In this article, the authors present a synthesis of the structures of three-phase machines with concentrated windings. (1) In the first part, the structures with a regular distribution of the slots are presented. A systematic method is proposed to determine the windings and the performances are discussed. (2) In the second part, the authors present original structures of three-phase machines with concentrated windings which use an irregular distribution of the slots. A specific method to identify these structures is described, and a comparative analysis of the performances of the original and traditional structures is performed by using a field calculation software.

570 citations


"Low Space Order Analysis of Radial ..." refers methods in this paper

  • ...The winding pattern is designed using a star of slots methodology [18], and Dogan et al....

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Book
12 Dec 2005-
Abstract: GENERATION AND RADIATION OF NOISE IN ELECTRICAL MACHINES Vibration, Sound, and Noise Sound Waves Sources of Noise in Electrical Machines Energy Conversion Process Noise Limits and Measurement Procedures for Electrical Machines Deterministic and Statistical Methods of Noise Prediction Economical Aspects Accuracy of Noise Prediction MAGNETIC FIELDS AND RADIAL FORCES IN POLYPHASE MOTORS FED WITH SINUSOIDAL CURRENTS Construction of Induction Motors Construction of Permanent Magnet Synchronous Brushless Motors A.C. Stator Windings Stator Winding MMF Rotor Magnetic Field Calculation of Air Gap Magnetic Field Radial Forces Other Sources of Electromagnetic Vibration and Noise INVERTER-FED MOTORS Generation of Higher Time Harmonics Analysis of Radial Forces for Nonsinusoidal Currents Higher Time Harmonic Torques in Induction Machines Higher Time Harmonic Torques in Permanent Magnet (PM) Brushless Machines Influence of the Switching Frequency of an Inverter Noise Reduction of Inverter-Fed Motors TORQUE PULSATIONS Analytical Methods of Instantaneous Torque Calculation Numerical Methods of Instantaneous Torque Calculation Electromagnetic Torque Components Sources of Torque Pulsations Higher Harmonic Torques of Induction Motors Cogging Torque in Permanent Magnet (PM) Brushless Motors Torque Ripple Due to Distortion of EMF and Current Waveforms in Permanent Magnet (PM) Brushless Motors Tangential Forces vs. Radial Forces Minimization of Torque Ripple in PM Brushless Motors STATOR SYSTEM VIBRATION ANALYSIS Forced Vibration Simplified Calculation of Natural Frequencies of the Stator System Improved Analytical Method of Calculation of Natural Frequencies Numerical Verification ACOUSTIC CALCULATIONS Sound Radiation Efficiency Plane Radiator Infinitely Long Cylindrical Radiator Finite Length Cylindrical Radiator Calculations of Sound Power Level NOISE AND VIBRATION OF MECHANICAL AND AERODYNAMIC ORIGIN Mechanical Noise Due to Shaft and Rotor Irregularities Bearing Noise Noise Due to Toothed Gear Trains Aerodynamic Noise Mechanical Noise Generated by the Load ACOUSTIC AND VIBRATION INSTRUMENTATION Measuring System and Transducers Measurement of Sound Pressure Acoustic Measurement Procedure Vibration Measurements Frequency Analyzers Sound Power and Sound Pressure Indirect Methods of Sound Power Measurement Direct Method of Sound Power Measurement: Sound Intensity Technique Standard for Testing Acoustic Performance of Rotating Electrical Machines NUMERICAL ANALYSIS Introduction FEM Model for Radial Magnetic Pressure FEM for Structural Modeling BEM for Acoustic Radiation Discussion STATISTICAL ENERGY ANALYSIS Introduction Power Flow Between Linearly Coupled Oscillators Coupled Multimodal Systems Experimental SEA Application to Electrical Motors NOISE CONTROL Mounting Standard Methods of Noise Reduction Active Noise and Vibration Control APPENDIX A: BASICS OF ACOUSTICS Sound Field Variables and Wave Equations Sound Radiation from a Point Source Decibel Levels and Their Calculations Spectrum Analysis APPENDIX B: PERMEANCE OF NONUNIFORM AIR GAP Permeance Calculation Eccentricity Effect APPENDIX C: MAGNETIC SATURATION APPENDIX D: BASICS OF VIBRATION A Mass-Spring-Damper Oscillator Lumped Parameter Systems Continuous Systems SYMBOLS AND ABBREVIATIONS BIBLIOGRAPHY INDEX

375 citations


"Low Space Order Analysis of Radial ..." refers background in this paper

  • ...Each harmonic of this radial pressure is well known [2], [3], [5], [11], for example, coupled with the interaction between the slotting and the magnetomotive force (MMF), or the saturation effect [4], [6]....

    [...]

  • ...This source of audible noise arises when Maxwell pressures induce dynamic deflections of the external structure (stator or rotor), which then propagate in the ambient air as acoustic waves [1], [2]....

    [...]

  • ...According to (1), it also determines BaR(t, αs) and Bpm(t, αs), the armature and magnet radial flux density, respectively [2]....

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Journal ArticleDOI
Zi-Qiang Zhu1, Lijian Wu1, Z.P. Xia1Institutions (1)
TL;DR: An accurate analytical subdomain model for computation of the open-circuit magnetic field in surface-mounted permanent-magnet machines with any pole and slot combinations, including fractional slot machines, accounting for stator slotting effect is presented.
Abstract: The paper presents an accurate analytical subdomain model for computation of the open-circuit magnetic field in surface-mounted permanent-magnet machines with any pole and slot combinations, including fractional slot machines, accounting for stator slotting effect. It is derived by solving the field governing equations in each simple and regular subdomain, i.e., magnet, air-gap and stator slots, and applying the boundary conditions to the interfaces between these subdomains. The model accurately accounts for the influence of interaction between slots, radial/parallel magnetization, internal/external rotor topologies, relative recoil permeability of magnets, and odd/even periodic boundary conditions. The back-electromotive force, electromagnetic torque, cogging torque, and unbalanced magnetic force are obtained based on the field model. The relationship between this accurate subdomain model and the conventional subdomain model, which is based on the simplified one slot per pole machine model, is also discussed. The investigation shows that the proposed accurate subdomain model has better accuracy than the subdomain model based on one slot/pole machine model. The finite element and experimental results validate the analytical prediction.

315 citations


"Low Space Order Analysis of Radial ..." refers methods in this paper

  • ...2589924 Analytical models (permeance/MMF and winding function approaches) [3], [5], semianalytical subdomain models [9], and the finite-element (FE) method can be used to evaluate the airgap flux density....

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Book
01 Jan 1989-
Abstract: A. Generation and Elimination of Noise and Vibration. 1. Basic acoustic terms. 2. Generation process of noise and vibration in electrical machines. 3. Electromagnetic noise and causes of vibration. 4. Vibration of rotating electrical machines. 5. Generation of airborne noise in electrical machines. 6. The effect of changes in running condition on the noise of rotating electrical machines. 7. Design considerations to reduce noise and vibration of electromagnetic origin. 8. Mechanical noise and vibrations. 9. Noises of aerodynamic origin. 10. Secondary noise reducing measures. B. Experimental Investigation of Noise and Vibration Phenomena. 11. Measuring noise and vibration phenomena. 12. Measuring the steady-state vibrations of electrical machines. 13. Noise measurements on electrical machines under steady-state operating conditions. 14. Measuring transient noise phenomena. 15. Measuring techniques of transient vibroacoustic signals. 16. Indirect measuring of transient vibroacoustic signals. C. Some Practical Applications of Vibroacoustic Methods in the Testing of Rotating Electrical Machines. 17. Noise and vibration testing in practice. 18. Applying vibration measurement to assessing the technical condition of rotating machines and to scheduling their maintenance. Epilogue with economic considerations. Appendices. References. Subject Index.

228 citations


"Low Space Order Analysis of Radial ..." refers background in this paper

  • ...This source of audible noise arises when Maxwell pressures induce dynamic deflections of the external structure (stator or rotor), which then propagate in the ambient air as acoustic waves [1], [2]....

    [...]


Performance
Metrics
No. of citations received by the Paper in previous years
YearCitations
20193
20182